Already looking vulnerable following a run of three defeats in their previous four Premier League matches, the 60-year-old saw his team comfortably bettered by Ole Gunnar Solskjaer's side at Stamford Bridge in the FA Cup.
As a result, Sarri has been made the red-hot sack race favourite and the latest update from Goal's Chelsea correspondent Nizaar Kinsella suggests the Italian has three matches to save his job.
A home game against Malmo should be straightforward for the Blues but tougher tests await with the Carabao Cup final against Manchester City on Sunday followed by the visit of Tottenham in the Premier League on February 27.
William Hill have odds on the next permanent Chelsea manager with the market led by Zinedine Zidane at 6/5 (2.20).
While that's understandable based on the former Real Madrid boss being one of the highest-profile candidates in the managerial sphere, such an appointment might take a relatively long time and might not be possible in the middle of an ongoing campaign.
The Blues might opt for a short-term interim boss to see them through to the end of the season with an internal candidate looking the most likely route.
As per the rules on William Hill's site, any caretaker or interim appointment will be deemed winners if they are to take charge for 10 competitive games or if the club indicate the manager will be appointed to cover 10 or more games.
Even after the Spurs clash, there will be 10 games of the Premier League campaign to go plus any additional Europa League clashes should Chelsea qualify against Malmo on Thursday.
With that in mind the 5/1 (6.0) about Gianfranco Zola looks the best value option at this stage. The current assistant first-team coach could be the go-to man to take over until the end of the current campaign if Sarri departs and therefore looks overpriced at 5/1 (6.0) with William Hill.
With the Rams in the promotion hunt though, it seems more likely that even if Lampard were to be under consideration, the Blues' all-time leading scorer would be another candidate for the end of the current campaign.
Having been sacked by Manchester United earlier in the campaign, Jose Mourinho is 12/1 (13.0) to make what would be a remarkable return to the club which he has already managed twice.
The Portuguese left under a cloud in December 2015 and it seems extremely unlikely that the Stamford Bridge hierarchy would look to the 56-year-old as a replacement for Sarri, if one were to be required.